Circuit, System and Method for Communication Between Two Nodes of a Radio Network

ABSTRACT

A first node of a radio network initiates a mode for finding the range to a second node. The first node transmits to the second node, with the address of the second node, a range finding command, which switches the second node into the range finding mode and controls a sequence. The first node transmits in a transmission time window a first signal, which is received by the second node in an associated reception time window, a first phase value of the first signal being measured. The second node transmits in a transmission time window a second signal, which is received by the first node in an associated reception time window, a second phase value of the second signal being measured. The first frequency is changed by a frequency difference and the second frequency is changed by the frequency difference in a subsequent time window of the sequence.

This nonprovisional application claims priority to German PatentApplication No. 10 2008 063 253.8, which was filed in Germany on Dec.30, 2008, and to U.S. Provisional Application No. 61/141,520, which wasfiled on Dec. 30, 2008, and which are both herein incorporated byreference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention concerns a circuit, a system, and a method forcommunication between two nodes of a radio network.

2. Description of the Background Art

In a radio network, it is desirable to find the position of the nodes ofthe radio network or at least to determine a distance between the nodes.By this means, a faulty node can be found easily, for example. Inaddition, slow movements of a node, such as of a means of transport in afactory, can be tracked. Position finding can also be used infirefighting when the nodes dropped from an airplane report alocation-specific elevated temperature.

Known from U.S. Pat. No. 5,220,332 is a range finding system with aninterrogator and a transponder that permits non-simultaneousmeasurements between two objects. A carrier signal is modulated with a(low-frequency) modulation signal with a variable modulation frequencyin order to determine a distance between the interrogator and thetransponder from the change in the modulation signal by means of a phasemeasurement or alternatively a transit time measurement.

From WO 02/01247 A2 is known a method for measuring distance between twoobjects using electromagnetic waves. An interrogation signal from a basestation and a response signal from a portable code transmitter aretransmitted twice at different carrier frequencies. In this system, thecarrier frequencies are correlated, which is to say that they aredependent on one another. The carrier frequencies are matched to oneanother so that a phase shift between the signals can be measured. Thedistance of the code emitter from the base station is calculated fromthis phase shift. The interrogation signal and the response signal canbe transmitted at different carrier frequencies or at the same carrierfrequency.

If a transceiver of a node for a sensor network is designed inconformance with the industry standard IEEE 802.15.4, then thetransceiver cannot simultaneously transmit and receive.

From U.S. Pat. No. 6,731,908 B2 is known a method for determining thedistance between two objects for the Bluetooth technology. In thismethod, the frequency is changed by frequency hopping in order tomeasure a phase offset for multiple different frequencies. An object hasa voltage controlled crystal oscillator in a phase locked loop (PLL),wherein the phase locked loop is closed during reception and openedduring transmission so that the receive signal and transmit signal havethe same frequency. The phase of the local oscillator signal of thevoltage controlled crystal oscillator is coherent with the receivedsignal due to the synchronization by means of the PLL.

SUMMARY OF THE INVENTION

It is therefore an object of the invention to improve a method forcommunication between two nodes of a radio network to the greatestextent possible.

Accordingly, a method for communication between two nodes of a radionetwork is provided that preferably conforms with the industry standardIEEE 802.15.4.

In the method, range finding is initiated by a first node of the radionetwork. The range finding can be initiated during setup of the radionetwork, for example. Alternatively, the range finding is carried outrepeatedly in order to determine a movement of a node. The range findingis initiated by a first node here. A phase measurement is carried out todetermine the distance. In order to take into account a multipathpropagation, the phase measurement is preferably carried out formultiple frequencies.

In a method step, a command (RRC—Ranging Request Command) for rangefinding with the address of the second node is transmitted from thefirst node to the second node in the range finding mode. The command forrange finding is preferably transmitted from the first node to thesecond node in the payload data of a frame.

In a method step, the second node is switched from an operating mode,for example a normal mode, into a range finding mode, by the rangefinding command. Preferably the second node carries outrange-finding-specific functions in the range finding mode that aredeactivated in the normal mode.

In the range finding mode, a sequence is controlled by the command. Thesequence provides multiple time windows in which method steps takeplace. The sequence in both nodes is controlled by the command.

As a result of the control by the command, a first signal is transmittedby the first node in a transmission time window of the sequence. Thefirst signal is received by the second node in a reception time windowof the sequence associated with the transmission time window, and afirst phase value of the first signal is measured.

As a result of the control by the command, a second signal istransmitted by the second node in a transmission time window of thesequence. The second signal is received by the first node in a receptiontime window of the sequence associated with the transmission timewindow, and a second phase value of the second signal is measured.

As a result of the control by the command, the first frequency of thefirst signal is changed by a frequency difference and the secondfrequency of the second signal is changed by the frequency difference ina time window following the transmission and reception time windows. Thechange in the first frequency and the change in the second frequencytake place in the same direction here. In this process, the firstfrequency and the second frequency are increased by the frequencydifference or the first frequency and the second frequency are decreasedby the frequency difference.

The invention has the additional object of specifying a circuit of anode of a radio network that is improved to the greatest degreepossible.

Accordingly, a circuit of a node of a radio network is provided, whichpreferably conforms with the industry standard IEEE 802.15.4. Preferablythe circuit has a transmitting/receiving circuit (transceiver) fortransmitting and receiving payload data within the radio network.Preferably the circuit is monolithically integrated on a semiconductorchip.

The circuit is designed for address-dependent reception of a rangefinding command. To this end, the hardware functions and softwarefunctions corresponding to the command are implemented in the circuit.The circuit preferably has the function of address decoding so thatrange finding commands that are not addressed to the circuit arerejected.

The circuit is designed such that the circuit can be switched into arange finding mode by the received command. Program sections andfunctions for range finding implemented in the circuit that aredeactivated in the normal mode are preferably activated in the rangefinding mode.

The circuit is configured to control a sequence by the command. Thesequence provides multiple time windows in which method steps of aprogram sequence of the circuit take place.

The circuit is configured to transmit a first signal in a transmissiontime window of the sequence under control by the command. Preferably thefirst signal is an unmodulated carrier signal. An example of anunmodulated carrier signal is a high-frequency sinusoidal signal.

The circuit is configured to receive a second signal in a transmissiontime window of the sequence under control by the command. In addition,the circuit is configured to measure a first phase value of the secondsignal. Preferably the second signal is an unmodulated carrier signal.

The circuit is configured to change a first frequency of the firstsignal by a frequency difference in a time window of the sequencefollowing the reception time window.

The circuit is configured to change the reception frequency undercommand control. The change here is by the magnitude of the frequencydifference. The reception frequency has the altered frequency for thereception of the second signal in another, subsequent reception timewindow of the sequence. The change in the first frequency and the changein the second frequency take place in the same direction here. In thisprocess, the first frequency and the second frequency are increased bythe frequency difference or the first frequency and the second frequencyare decreased by the frequency difference.

Another aspect of the invention is a radio network system, in particularaccording to the industry standard IEEE 802.15.4. The system has a firstnode and at least one second node. Preferably at least one of the secondnodes has a circuit described above.

The first node of the system is configured for initiating a mode for themeasurement of a distance to the second node. The first node isconfigured for transmitting to the second node a range finding commandwith the address of the second node. The second node can be switchedinto a range finding mode by the command.

In the range finding mode, the first node and the second node areconfigured to control a sequence in both nodes by the command. Thesequence provides multiple time windows in which method steps of aprogram of the circuit take place.

As a result of the control by the command, the first node is configuredto transmit a first signal in a transmission time window of thesequence, and the second node is configured to receive the first signaland to measure a first phase value of the first signal in an associatedreception time window of the sequence.

As a result of the control by the command, the second node is configuredto transmit the second signal in a transmission time window of thesequence, and the first node is configured to receive the second signaland to measure a second phase value of the second signal in anassociated reception time window of the sequence.

The first node is configured to change the first frequency of the firstsignal by a frequency difference in a time window of the sequence. Thesecond node is configured to change the second frequency of the secondsignal likewise by the frequency difference. The change in the firstfrequency and the change in the second frequency take place in the samedirection here. In this process, the first frequency and the secondfrequency are increased by the frequency difference or the firstfrequency and the second frequency are decreased by the frequencydifference.

The refinements described below relate equally to the method, thecircuit, and the system. Functional features of the circuit or of thesystem derive from features of the method here. Method features can alsobe derived from functions of the circuit or of the system.

According to an advantageous embodiment, provision is made for thetransmission time window and reception time window to be repeated afterthe time window for changing the first frequency of the first signal andthe second frequency of the second signal. With the repetition, a thirdphase value of the first signal and a fourth phase value of the secondsignal are measured. Preferably the distance is calculated from thefirst phase value, second phase value, third phase value, fourth phasevalue, and the frequency difference. Preferably exactly one distancevalue is calculated from the first phase value, second phase value,third phase value, fourth phase value, and the frequency difference.

In order to take into account a multipath propagation, in particular,provision is preferably made for the transmission time window, receptiontime window, and time window for changing the first and secondfrequencies to be repeated for a plurality of different firstfrequencies and a plurality of different second frequencies.

According to an embodiment, a sequence of the first and/or secondfrequency for range finding is transmitted to the second node with therange finding command.

In an embodiment, provision is made that a frame for synchronizing astart time for the range finding is transmitted from the second node tothe first node. As a result of the synchronization, a first methodsequence in the first node and a second method sequence in the secondnode are coordinated with one another in time. Preferably a timesynchronization of the transmission time windows and reception timewindows of the sequence in the first node and the node takes place as aresult of the control by the command. Preferably the timesynchronization achieves the result that a transmission time window andan associated reception time window are simultaneous with apredetermined precision of, for example, 1 μs.

According to an embodiment, a first timer is started by the first nodeas a function of a reception time of the frame for synchronization.Preferably a second timer is started by the second node as a function ofa transmission time of the frame for synchronization. The reception timeand/or the transmission time relate to a position within the frame, forexample the end of the frame or the beginning of the payload data or anindicator within the frame. Since the length of the frame is known bythe first node and the second node, the position for the reception timeor the position for the transmission time within the frame can be agreedby the first node and by the second node.

Preferably the sequence is started in both nodes in a synchronizedmanner by the first node upon expiration of the first timer and by thesecond node upon expiration of the second timer. Steps of the sequencein the first node correspond in time to steps of the sequence in thesecond node here. For example, multiple different frequencies are usedsequentially for range finding. The switch between two frequencies inthe first node and in the second node is coordinated in time as a resultof the synchronization within an agreed time window, for example.

In an embodiment, the second node transmits an acknowledgment (ACK) backto the first node after the successful reception of the range findingcommand. Upon receiving the acknowledgment, the first node is ready forthe range finding, and preferably switches its receiver over. With theswitchover, the first node is preferably configured to receive asynchronization frame with an altered indicator.

According to an embodiment, an indicator (SFD—Start of Frame Delimiter)contained in a frame is changed by the first node to flag payload data(PSDU) of a frame to be decoded that follows the indicator. Preferablythe indicator is changed to a value associated with the range findingcontrolled by the command (RRC). The value preferably is notstandard-conformant here. It is likewise possible to switch the firstnode to the altered indicator immediately after transmitting the rangefinding command, so that the second node would not have to send anacknowledgment. In this case, the first node would have a timeoutcounter to monitor whether the second node is configured for rangefinding. In the absence of a synchronization frame from the second node,the first node would terminate the range finding mode.

According to an embodiment, the second node transmits a frame, inparticular the synchronization frame, with the altered indicator valuein the range finding mode. Since the value of the indicator is notstandard-conformant, higher layers of uninvolved nodes are not occupiedwith the analysis thereof. In contrast, the first node preferablyanalyzes the reception of the frame for synchronization in higher layersin the range finding mode. In advantageous manner, the first nodeimmediately resets the indicator to a standard value after receiving thesynchronization frame.

According to an embodiment, provision is made that measurement resultsof the range finding are transmitted from the second node to the firstnode. The transmission of the measurement results takes place after thecompletion of the range finding, preferably by means of payload data ofa standard-conformant frame. The indicator is preferably reset to astandard-conformant value for transmission.

Preferably provision is made that the range finding command istransmitted in a secured manner, in particular encrypted.

Parameters can be transmitted along with the range finding command. Thealtered value of the indicator and/or a sequence of frequencies for therange finding and/or a time duration for one or more sequence steps ofthe range finding are transmitted to the second node with the rangefinding command. The transmission advantageously takes place withpayload data of a frame transmitted in a standard-conformant manner.

Further scope of applicability of the present invention will becomeapparent from the detailed description given hereinafter. However, itshould be understood that the detailed description and specificexamples, while indicating preferred embodiments of the invention, aregiven by way of illustration only, since various changes andmodifications within the spirit and scope of the invention will becomeapparent to those skilled in the art from this detailed description.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given hereinbelow and the accompanying drawingswhich are given by way of illustration only, and thus, are not limitiveof the present invention, and wherein:

FIG. 1 is a schematic representation of a radio network with nodes A, B,C, and D,

FIG. 2 is a schematic diagram for synchronization, and

FIG. 3 is a schematic flowchart for range finding in a radio network.

DETAILED DESCRIPTION

FIG. 1 is a schematic representation of a radio network in accordancewith the industry standard IEEE 820.15.4 with nodes A, B, C, and D. Thenodes A, B, and C are designed to use a standard-conformant (MAC)command RRC from the range of reserved IEEE 820.15.4 MAC command IDs forrange finding. In contrast, the node D has no function for rangefinding.

In the exemplary embodiment in FIG. 1, node A is the initiator of therange finding of the distance dAB to node B. The target address of nodeB is known to node A. In the radio network in the exemplary embodimentin FIG. 1, node A is authorized to communicate directly with node B.Node A will trigger the post-processing of the measured data. Thepost-processing here includes measured data from node A and alsomeasured data M (SFD) from node B.

The node A sends a range finding command RRC to the node B. For theactual range finding, a synchronization of a sequence in the node A anda sequence in the node B is advantageous. To this end, the node B sendsa synchronization frame Fsync (SFD′) to the node A.

A schematic flowchart for range finding is shown in FIG. 3. In step 1,node A starts range-finding by starting a sequence. Following a standardprocedure CSMA-CA in step 2.1 for determining whether a channel can beallocated for transmission, in step 2.2 a command RCC for starting thesequence for range finding is transmitted from node A to node B with thetarget address. A sequence of frequencies/channels or a target value ofan indicator SFD can be included in the transmission to node B aspayload data here. The command RRC is encoded as a MAC command frame,with the command ID being configurable. The command ID is from the rangeof reserved values 3′b100 . . . 3′b111.

The command RRC is preferably transmitted in a secured manner. To thisend, an encryption can be used, for example. A frequency hop sequence istransmitted with the frame. For example, the sequential frequency valuesor an index to the hop sequences stored in the nodes A and B can betransmitted for this purpose. As a result of the secured transmission,the sequence of the frequencies—in particular of an unmodulated carriersignal—within the measurements in the frequency range is not known topossible attackers, which makes interfering more difficult.

In step 3.1, the node B detects a match between the target address andits ID, and in step 3.2 extracts the information for the range findingcontained in the payload data of the received frame. In step 3.3, thecommand RRC and the header with frame address are checked by node B andan acknowledgment of reception is returned to node A. Node A receivesthe acknowledgment and continues the range finding mode with the startof a sequence for range finding. Otherwise node A terminates the rangefinding mode in the absence of an acknowledgment or initiates it anew toanother node. With the reception of the acknowledgment, node A switches'its receiver over, to be able to receive a synchronization frame withaltered indicator SFD. In addition, after transmitting theacknowledgment, node B transmits a synchronization frame with alteredindicator SFD′, which accordingly can only be received by node A. Incontrast, nodes C and D reject the frame with the altered,non-standard-conformant indicator SFD′.

As a result of this selection, the selection of the participants for therange finding, namely nodes A and B, within the radio network iscompleted. Node C cannot associate the target address with its ID instep 3 c. Node D does not recognize the range finding command RRC instep 3 d and accordingly does not react.

Node B adopts the hop sequence after decrypting the payload data andprepares itself for the measurement sequence. The measurement sequenceproceeds synchronously in nodes A and B with an error of +/−1 μs, forexample.

In step 4, node A changes its indicator SFD to a non-standard-conformantvalue, which is to say not equal to 0x00 and not equal to 0xA7.

Following a standard procedure for channel allocation (CSMA-CA) in step5.1, in step 5.2 node B sends an empty frame for synchronization to nodeA with the altered value of the indicator. The modified value of theindicator prevents other network participants C and D from receivingthis frame and being able to interfere. In accordance with FIG. 2, nodeB starts the measurement sequence in step 8 after expiration of a timerwith the timer time tB, wherein the timer is started at the transmittime tFsync and expires at the time tM, the starting time of themeasurement sequence.

In step 6.1 of FIG. 3, the synchronization frame is received by node A.The synchronization frame is used by node A at the PHY layer (physicallayer)—also called the bit transmission layer in the OSI layer model—asa specific start signal for the measurement sequence in step 8. Inaccordance with FIG. 2 the node A starts the measurement sequence instep 8 after expiration of a timer with the timer expiration time tA,wherein the timer is started at the reception time tE and expires at thetime tM, the starting time of the measurement sequence. In the exemplaryembodiment from FIG. 2, the timer is started with the end of the payloaddata PSDU of the received frame. Two alternatives are likewise shown inFIG. 2, wherein the timer could be started at the time tE′ after theindicator or at the time tE″ after the preamble SHR. In all cases, thetimer would likewise, have to expire at the time tM in order to achievetime synchronization with the node B. The accuracy of thesynchronization here is dependent, in particular, on the accuracy of thetwo timers and on the transmission distance.

In addition, in step 6.1 node A resets the indicator to thestandard-conformant value 0xA7. Node A sends an acknowledgment in step6.2, which is received and checked by node B in step 7.

In step 8 the measurement sequence for node A and for node B is carriedout within the time period N*tm. The measurement sequence 8 has atransmission time window 8 a.1 of the node A, which can also be referredto as a transmission phase. Synchronous herewith, the measurementsequence 8 has an associated reception time window 8 b.1 of the node B,which can also be referred to as a reception phase. The measurementsequence 8 has a transmission time window 8 b.2 of the node B.Synchronous herewith, the measurement sequence 8 has an associatedreception time window 8 a.2 of the node A. In the time window 8 a.3 or 8b.3, the frequency, for example the carrier frequency of an unmodulatedcarrier signal, is changed and the step 8 is repeated N times until ameasurement of a phase value in the applicable node has been carried outfor as many of the frequencies of the sequence as possible.

For the measurement, short bursts are transmitted in alternation andphase relationships and/or amplitude relationships are measured andstored in both node A and node B.

Following a standard procedure for channel allocation in step 9.1, instep 9.2 the measurement results of node B are transmitted back to nodeA with a standard-conformant frame. The payload data are secured for thetransmission. The payload data contents are the amplitude and/or phasevalues from the measurement in node B.

In steps 10.1 and 10.2 node A receives the measured data from node B,initiates an analysis of the measured data for calculating the distancedAB between the nodes A and B, and in step 10.3 transmits anacknowledgment back to node B, which is received and checked by node Bin step 10. 4. In contrast, nodes C and D were unable to detect a matchbetween the target address and their IDs in steps 10 c and 10 d. Insteps 11 a and 11 b, the method for range finding is terminated and thenodes A and B switch to a normal mode.

The invention is not restricted to the variant embodiments shown inFIGS. 1 through 3. For example, it is possible to use different timerstart points. It is also possible to specify the precise sequence offrequencies for range finding and/or the changed value of the indicator.In addition, it is also possible to provide the range finding in a radionetwork complying with a different industry standard, for example WLAN.

The invention being thus described, it will be obvious that the same maybe varied in many ways. Such variations are not to be regarded as adeparture from the spirit and scope of the invention, and all suchmodifications as would be obvious to one skilled in the art are to beincluded within the scope of the following claims.

1.-13. (canceled)
 14. A method for communication between two nodes of aradio network, the method comprising: transmitting, by the first nodeand to a second node, a first signal at a first frequency, the firstsignal transmitted during a first time window and having a measurablefirst phase value; receiving, by the first node, a second signal fromthe second node, the second signal received at a second frequency, thesecond signal received during the first time window and having ameasurable second phase value; transmitting, by the first node and tothe second node, a third signal at a third frequency that is differentfrom the first frequency by a frequency difference, the third signaltransmitted during a second time window and having a measurable thirdphase value; receiving, by the first node, a fourth signal from thesecond node, the fourth signal received at a fourth frequency that isdifferent from the second frequency by the frequency difference, thefourth signal received during the second time window and having ameasurable fourth phase value; and based on the first phase value, thesecond phase value, the third phase value, and the fourth phase valueand the frequency difference, determining the distance between the firstnode and the second node.
 15. The method according to claim 14, furthercomprising: receiving, by the first node and from the second node, thefirst phase value of the first signal; measuring, by the first node, thesecond phase value of the second signal; receiving, by the first nodeand from the second node, the third phase value of the third signal; andmeasuring, by the first node, the fourth phase value of the fourthsignal.
 16. The method according to claim 15, wherein the first phasevalue and the third phase value are received from the second node afterthe fourth signal is received.
 17. The method according to claim 14,wherein: the first frequency and the second frequency are the same; andthe third frequency and the fourth frequency are the same.
 18. Themethod according to claim 14, further comprising transmitting, by thefirst node, a range finding command to an address of the second node,the range finding command identifying a sequence of the first frequency,the second frequency, the third frequency, and the fourth frequency. 19.The method according to claim 18, wherein the range finding command isencrypted when transmitted by the first node to the second node.
 20. Themethod according to claim 14, further comprising transmitting a command,from the first node to the second node, wherein the command synchronizesa start time of the first time window.
 21. The method according to claim14, further comprising: changing, by the first node, an indicatorfollowing payload data of a frame to a value associated with rangefinding; transmitting, by the first node, the altered value of theindicator to the second node with a range finding command; andreceiving, by the first node and from the second node, a frame or asynchronization frame with an altered value of the indicator.
 22. Themethod according to claim 14, further comprising determining movement ofthe second node based on the distance measured between the first nodeand the second node.
 23. A first node of a radio network, the first nodecomprising: a circuit comprising a transceiver, the circuit configuredto: transmit, to a second node and during a first time window, a firstsignal at a first frequency, the first signal having a measurable firstphase value; receive, from the second node and during the first timewindow, a second signal at a second frequency, the second signal havinga measurable second phase value; transmit, to the second nod and duringa second time window, a third signal at a third frequency, the thirdfrequency separated from the first frequency by a frequency difference,the third signal having a measurable third phase value; receive, at afourth frequency and during a second time window, a fourth signal fromthe second node, the fourth frequency separated from the secondfrequency by the frequency difference, the fourth signal received havinga measurable fourth phase value; and based on the first phase value, thesecond phase value, the third phase value, and the fourth phase valueand the frequency difference, determine the distance between the firstnode and the second node.
 24. The first node according to claim 23,wherein the circuit is further configured to: receive the first phasevalue of the first signal from the second node; measure the second phasevalue of the second signal; receive the third phase value of the thirdsignal from the second node; and measure the fourth phase value of thefourth signal.
 25. The first node according to claim 24, wherein thefirst phase value and the third phase value are received from the secondnode after the fourth signal is received.
 26. The first node accordingto claim 23, wherein: the first frequency and the second frequency arethe same; and the third frequency and the fourth frequency are the same.27. The first node according to claim 14, wherein the circuit is furtherconfigured to transmit a range finding command to an address of thesecond node, the range finding command identifying a sequence of thefirst frequency, the second frequency, the third frequency, and thefourth frequency.
 28. The first node according to claim 27, wherein thecircuit is further configured to encrypt the range finding commandbefore transmitting the range finding command to the second node. 29.The first node according to claim 27, wherein the range finding commandsynchronizes a start time of the first time window for the first nodeand the second node.
 30. The first node according to claim 23, whereinthe circuit is further configured to: change an indicator followingpayload data of a frame to a value associated with range finding; andreceive, from the second node, a frame or a synchronization frame withan altered value of the indicator.
 31. The first node according to claim30, wherein the circuit is further configured to: transmit the alteredvalue of the indicator to the second node with a range finding command;and receive, from the second node, measurement results of the rangefinding from the second node, the measurement results comprising a resetvalue of the indicator.
 32. The first node according to claim 23,wherein the circuit is further configured to determine movement of thesecond node based on the distance measured between the first node andthe second node.
 33. A radio network system, comprising: a first node;and a second node, wherein the first node is configured to transmit, toa second node and during a first time window, a first signal at a firstfrequency, the first signal having a measurable first phase value,wherein, in response to receiving the first signal, the second node isconfigured to transmit, to the first node and during the first timewindow, a second signal at a second frequency, the second signal havinga measurable second phase value; wherein, in response to receiving thesecond signal, the first node is configured to transmit, to the secondnod and during a second time window, a third signal at a thirdfrequency, the third frequency separated from the first frequency by afrequency difference, the third signal having a measurable third phasevalue; wherein, in response to receiving the third signal, the secondnode is configured to transmit, at a fourth frequency and during thesecond time window, a fourth signal to the first node, the fourthfrequency separated from the second frequency by the frequencydifference, the fourth signal received having a measurable fourth phasevalue; wherein the first node is configured to determine the distancebetween the first node and the second node based on the first phasevalue, the second phase value, the third phase value, and the fourthphase value and the frequency difference.